Just from curiosity, I want to see whether my 1992 300D (224 k miles) has original engine and transmission.

Can I see the transmission number and the engine number without lifting the car?

I'm not sure exactly where to look for the engine number on your 92. If no one else knows I'm sure I can find out.
The transmission number is stamped into the side of the transmission case just above the transmission pan on the right (passenger) side.

Gilly